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A254333
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Squares (A000290) which are also centered pentagonal numbers (A005891).
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4
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1, 16, 1156, 22801, 1666681, 32878756, 2403352576, 47411143081, 3465632747641, 68366835443776, 4997440018745476, 98584929298781641, 7206305041398228481, 142159399682007682276, 10391486872256226723856, 204993755756525779060081, 14984516863488437537571601
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = a(n-1)+1442*a(n-2)-1442*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+15*x^3-302*x^2+15*x+1) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)).
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EXAMPLE
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16 is in the sequence because it is the 4th square number and the 3rd centered pentagonal number.
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MATHEMATICA
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LinearRecurrence[{1, 1442, -1442, -1, 1}, {1, 16, 1156, 22801, 1666681}, 20] (* Harvey P. Dale, Jul 26 2015 *)
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PROG
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(PARI) Vec(-x*(x^4+15*x^3-302*x^2+15*x+1) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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